gas is escaping a spherical ballon at the rate of 4cm per minute . how fast is the surface area shrinking when the radiusis 24cm?

Q: 8. If F(x)= dt, then F'(x)=

A: Using Leibnitz rule for integral.

Q: 6. sin v- -2 cos Va + C %3D 4x2 1. Ja-8 dx = 18 (1-8x)4 (1-8x3)4 8. Se*dx =+ %3D In e

A: As per the instruction, we will be answering only the first three subparts. For (6),    ∫sinxxdxLet…

Q: Question 7 Find the volume of the solid that results when the region enclosed by the given curves is…

A: We need to find volume of enclosed region.

Q: 2 sec" x AX JS -sec? x

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Q: QI// Find the Area bounded by: x = -y2 and x =y-2

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Q: 20-1 to -5 -10 Find the aren et he regpen endosad by Hhan gaco p he serkicd lie X =1 an2 %3D

A: Given the query is to find area enclosed bybthe curves.

Q: 3. Find the integral * dx a² -2 x+1 a.-x - - x - In(x + 1) + C 2 b.x2 – x – In(x + 1) + C c.x2 – x +…

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Q: Evaluate y' of the given functions y = /3x + 4)(x + 3)

A: We can find the derivative as below.

Q: Let f be a function defined by f(x) = In(2x? + 1) and let g be a function defined by g(x) = 2x4 -…

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Q: The graph of a derivativef'(x) is shown in the figure below. Fill in the table of values for /(x)…

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Q: 4–x? c1-a²-y² x dz dy dx = -7+x?+y?

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Q: Next, simplify. - 3t dt = dx

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Q: consider a function f (x) vihose derivative f"(x) is continuous as shown belowr. Graph of f'(x), NOT…

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Q: Find the average rate of change of the function from X1 to X2 Function x-Values f(x) = x2 - 4x + 6 X…

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Q: 24. Given z = 6x°y-e", calculate or z. A) 12y–x'e" B) 12y-ye" C) 12y-e" ху D) 12x - хуе"

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Q: Answer the question. Show ALL your steps in your calculations. Answer in complete sentences. 8…

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Q: x+2x2-3x x²+4x+3 2) Evaluate lim -6-1. x→ -3 Show every step.

A: We can solve this as follows:

Q: Find the local linear approximation L (x) of the function f(æ) = 5 – a² at x= 2.

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Q: 2 Compute limx→16; 1-x2 1 X-1

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Q: Find the differential dy of the given function. (Use "dx" for dx.) x + 1 4x - 7 dy

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Q: Vx-5 1) Evaluate lim 10. x25 X-25 Show every step.

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Q: Let C(x) =x +4x+1 dollars be the cost function, where the x represents the quantity. The !3!…

A: 1) Here, to find the 11th item.  Now, the cost of x quantity is given by: C(x)=25x2+4x+1

Q: Evaluate y' of the given functions: 1 Find y"'for y (x+4)3

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Q: Question 6 Use cylindrical shells to find the volume of the solid generated wher the region enclosed…

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Q: d а. dx (e* cos.x) cOs x

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: Find the vector

A: The vector r=<a,b> is written as, r(i)=ai+ bj

Q: 1. Suppose a car is travelling on a straight road and s(t) is the distance travelled after For…

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Q: Let f(x) = (8x2 + 6x + 11)/(7 - 7x²). The horizontal asymptote is given by y = ? Round your answer…

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Q: A ball is thrown vertically upward from the top of the house 112 ft high with an initial velocity of…

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Q: A MANUFACTURER NEEDS TO MAKE A CYLINDRICAL CAN THAT WILL HOLD 1.5LITRES OF LIQUID. Determine the…

A: Follow the procedure given below.

Q: 2. Use the Laplace transform to solve the initial value problem y" + 4y' + 5y = 2, y(0) = -2, y'(0)…

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Q: Find the nth derivative of y = In(16x2 – 9).

A: Given y=ln(16x2-9)

Q: Use the divergence theorem to find the outward flux of F across the boundary of the region D. F=…

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Q: Given that å = i+ 53 -3k and b = 3ỉ – 23 +k are vectors in 3D. Find the value of ả x b and b xả…

A: Given; a→=i→+5j→-3k→, b→=3i→-2j→+k→

Q: y varies inversely as the fourth root of x and when x = 81, y = 10. What would be y when x-45. Round…

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Q: a²z Determine if z = tan- + r2+02° r

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Q: 5 ,2 X |x² + x – 6| dx -5

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Q: 1. Find the derivative of the following: (Simplify your final answers.) sech h. j(r) = e (Using…

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Q: Let й -, й- where A and Bare some constants. Given that ü+ 50 = find the value of the product A.B.…

A: A. B=48

Q: Use L'Hôpital's rule to evaluate the following limit sin(x) lim

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Q: Evaluate y' of the given functions: 1. y = (x² – 2)(x + 3)

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Q: Show that whether x5 + 10x3 + x + 1 is O(x4) or not?

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: Given region is bounded by y=21-2x and y=20

Q: Derivative of f(x) and derivative of g(x) are equal. Then f(x) = g(x). %3D Select one: O True False

A: Answer is given with example.

Q: 10) Find T4(x), the degree 4 taylor polynomial of the function for f(x) = cos(5x) centred at c = 2n…

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Q: If 0 < 0 < 7, which of the following points DOES NOT coincide with the polar point (-r, 0)? Select…

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Q: 3-A coin is tossed 3 times the probability that all 3 tosses are tail equal a) b); c); d) 9.

A: Our Aim is to calculate the probability of flipping a coin three times andgettiing 3 tails.

Q: Given the series E Vn9 +1 Vn9 1. n=1 Explain why the limit comparison test is applicable to check…

A: Using limit comparision and p test.

Q: j(r) = e sech

A: The given function,      jr=esechr2+2r

Q: y = e2a %3D

A: